I'm getting confused on this problem, such as when to use dy and dx. If someone can please help me solve these problems and explain them, I would greatly appreciate it. Thank you.

Find the surface area generated by revolving the region bounded by the curve y = -x^2 + 5 and in the first quadrant about the
a) y-axis
b) x-axis
c) line x = -1

The surface area rotating about the x-axis is given by:
But the formula for rotating about the y-axis is not taught.
However is you really want to, you can think of:
As, (rotate graph counterclickwise)
Thus,